10. Consider an MA process x(n) of order two described by the difference equation x(n) = v(n) + 0.75 v(n − 1) + 0.75 v(n − 2), where v(n) is a zero-mean white-noise process of unit variance. The requirement is to approximate this process by an AR process u(n) of order M. Do this approximation for the following orders: (a) M = 2. (b) M=5. (c) M = 10. Comment on your results. How big would the order M of the AR process u(n) have to be for it to be equivalent to the MA process x(n) exactly?

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10. Consider an MA process x(n) of order two described by the difference equation
x(n) = v(n) + 0.75 v(n – 1) + 0.75 v(n – 2),
where v(n) is a zero-mean white-noise process of unit variance. The requirement is to approximate
this process by an AR process u(n) of order M. Do this approximation for the following orders:
(a) M=2.
(b) М -5.
(с) М— 10.
Comment on your results. How big would the order M of the AR process u(n) have to be for
it to be equivalent to the MA process x(n) exactly?
Transcribed Image Text:10. Consider an MA process x(n) of order two described by the difference equation x(n) = v(n) + 0.75 v(n – 1) + 0.75 v(n – 2), where v(n) is a zero-mean white-noise process of unit variance. The requirement is to approximate this process by an AR process u(n) of order M. Do this approximation for the following orders: (a) M=2. (b) М -5. (с) М— 10. Comment on your results. How big would the order M of the AR process u(n) have to be for it to be equivalent to the MA process x(n) exactly?
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